A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada–Watanabe argument. Similar results are also proved for the Fleming–Viot process.
"Super-Brownian motion as the unique strong solution to an SPDE." Ann. Probab. 41 (2) 1030 - 1054, March 2013. https://doi.org/10.1214/12-AOP789